Here are all the packages needed to get started.

library(gt)
library(tidyverse)
library(gtsummary)
library(plotly)
library(readxl)
library(plotly)
library(corrplot)




sessionInfo()
## R version 4.2.1 (2022-06-23 ucrt)
## Platform: x86_64-w64-mingw32/x64 (64-bit)
## Running under: Windows 10 x64 (build 19045)
## 
## Matrix products: default
## 
## locale:
## [1] LC_COLLATE=English_United States.utf8 
## [2] LC_CTYPE=English_United States.utf8   
## [3] LC_MONETARY=English_United States.utf8
## [4] LC_NUMERIC=C                          
## [5] LC_TIME=English_United States.utf8    
## 
## attached base packages:
## [1] stats     graphics  grDevices utils     datasets  methods   base     
## 
## other attached packages:
##  [1] corrplot_0.92   readxl_1.4.2    plotly_4.10.1   gtsummary_1.7.1
##  [5] lubridate_1.9.2 forcats_1.0.0   stringr_1.5.0   dplyr_1.1.2    
##  [9] purrr_1.0.1     readr_2.1.4     tidyr_1.3.0     tibble_3.2.1   
## [13] ggplot2_3.4.2   tidyverse_2.0.0 gt_0.9.0       
## 
## loaded via a namespace (and not attached):
##  [1] tidyselect_1.2.0       xfun_0.39              bslib_0.4.2           
##  [4] colorspace_2.1-0       vctrs_0.6.2            generics_0.1.3        
##  [7] htmltools_0.5.5        viridisLite_0.4.2      yaml_2.3.7            
## [10] utf8_1.2.3             rlang_1.1.1            jquerylib_0.1.4       
## [13] pillar_1.9.0           glue_1.6.2             withr_2.5.0           
## [16] lifecycle_1.0.3        cellranger_1.1.0       munsell_0.5.0         
## [19] gtable_0.3.3           htmlwidgets_1.6.2.9000 evaluate_0.21         
## [22] knitr_1.42             tzdb_0.4.0             fastmap_1.1.1         
## [25] fansi_1.0.4            scales_1.2.1           cachem_1.0.8          
## [28] jsonlite_1.8.4         hms_1.1.3              digest_0.6.31         
## [31] stringi_1.7.12         grid_4.2.1             cli_3.6.1             
## [34] tools_4.2.1            magrittr_2.0.3         sass_0.4.6            
## [37] lazyeval_0.2.2         pkgconfig_2.0.3        broom.helpers_1.13.0  
## [40] data.table_1.14.8      xml2_1.3.4             timechange_0.2.0      
## [43] rmarkdown_2.21         httr_1.4.6             rstudioapi_0.14       
## [46] R6_2.5.1               compiler_4.2.1

1 Univariate Analysis

In univariate analysis, we look at a single variable and describe 3 different things:

  • Center
  • Shape
  • Spread

1.1 Center

Helps explain where the middle of the data is. This can be measured in 3 main ways.

1.1.1 Mean

grades <- c(78,79,80,81,82)

mean(grades)
## [1] 80

1.1.2 Median

median(grades)
## [1] 80

1.1.3 Mode

There isn’t an easy way of doing this, so I created a function instead.

getModes <- function(x) {
  ux <- unique(x)
  tab <- tabulate(match(x, ux))
  ux[tab == max(tab)]
}


getModes(grades)
## [1] 78 79 80 81 82

Since there is no value that occurs most frequently, they all show. Mode is rarely used.

1.2 Shape

For this, I am going to randomly generate 100 exam scores.

grades <- rnorm(100,mean = 75, sd = 5 )
hist(grades)

You can mess with the breaks = arguement to get different numbers of bins.

1.3 Spread

Let’s look at a different dataset. Starwars character heights.

var(starwars$height)
## [1] NA

What happened? We have nulls in our data, so we cannot calculate the variance until we tell the system to ignore null values

var(starwars$height, na.rm = TRUE)
## [1] 1208.983
sd(starwars$height, na.rm = TRUE)
## [1] 34.77043
IQR(starwars$height, na.rm = TRUE)
## [1] 24
range(starwars$height, na.rm = TRUE)
## [1]  66 264

1.3.1 Visualizing Spread

You can visualize the spread as well this with a boxplot.

boxplot(starwars$height)

You can see that a lot of them fall outside of the fences.

You could also visualize this with a histogram

hist(starwars$height, breaks = "fd")

1.4 Easier Way

To get most of the items of interest, you can simply use the summary() function. The standard deviation nor the variance is displayed, so you would still need those.

summary(mtcars)
##       mpg             cyl             disp             hp       
##  Min.   :10.40   Min.   :4.000   Min.   : 71.1   Min.   : 52.0  
##  1st Qu.:15.43   1st Qu.:4.000   1st Qu.:120.8   1st Qu.: 96.5  
##  Median :19.20   Median :6.000   Median :196.3   Median :123.0  
##  Mean   :20.09   Mean   :6.188   Mean   :230.7   Mean   :146.7  
##  3rd Qu.:22.80   3rd Qu.:8.000   3rd Qu.:326.0   3rd Qu.:180.0  
##  Max.   :33.90   Max.   :8.000   Max.   :472.0   Max.   :335.0  
##       drat             wt             qsec             vs        
##  Min.   :2.760   Min.   :1.513   Min.   :14.50   Min.   :0.0000  
##  1st Qu.:3.080   1st Qu.:2.581   1st Qu.:16.89   1st Qu.:0.0000  
##  Median :3.695   Median :3.325   Median :17.71   Median :0.0000  
##  Mean   :3.597   Mean   :3.217   Mean   :17.85   Mean   :0.4375  
##  3rd Qu.:3.920   3rd Qu.:3.610   3rd Qu.:18.90   3rd Qu.:1.0000  
##  Max.   :4.930   Max.   :5.424   Max.   :22.90   Max.   :1.0000  
##        am              gear            carb      
##  Min.   :0.0000   Min.   :3.000   Min.   :1.000  
##  1st Qu.:0.0000   1st Qu.:3.000   1st Qu.:2.000  
##  Median :0.0000   Median :4.000   Median :2.000  
##  Mean   :0.4062   Mean   :3.688   Mean   :2.812  
##  3rd Qu.:1.0000   3rd Qu.:4.000   3rd Qu.:4.000  
##  Max.   :1.0000   Max.   :5.000   Max.   :8.000

2 Bivariate Analysis

When looking at 2 variables, we use correlation, scatterplots, and time series graphs.

2.1 Correlation

cor(mtcars$mpg, mtcars$hp)
## [1] -0.7761684

These are strongly negatively correlated. We might say, horsepower has a inverse relationship with mpg, or mpg has a negative relationship with horsepower.

2.2 Scatterplots

We can also visualize this relationship with a scatterplot.

plot(mtcars$hp, mtcars$mpg)

we can also make this look nicer with some labels

plot(mtcars$hp, mtcars$mpg,
     main = "Scatterplot of Horsepower and Miles Per Gallon",
     xlab = "Horsepower",
     ylab = "Miles Per Gallon")

2.3 Time series graphs

Since the data we’ve seen thus far has been only cross section, let’s bring in the data from the previous module. Wealth1Percent.xlsx

Wealth1percent <- read_excel("../Data/Wealth1percent.xlsx",
                             col_types = c("date", "numeric","numeric"))

To add the trend line, we need to do something that we haven’t discussed yet. Don’t worry, I’ll explain it in the next module.

plot(Wealth1percent$quarter,Wealth1percent$Share, type = "l")
abline(lm(Share ~ quarter, data = Wealth1percent),lty = 2)

3 More Visual Displays!

Here are some more ways to display data

3.1 Data Tables

We can represent data in categorical fashion:

table(starwars$hair_color)
## 
##        auburn  auburn, grey auburn, white         black         blond 
##             1             1             1            13             3 
##        blonde         brown   brown, grey          grey          none 
##             1            18             1             1            37 
##       unknown         white 
##             1             4

Or quantitative

bins <- seq(10,34,by = 2)

mpg <- cut(mtcars$mpg,bins)

table(mpg)
## mpg
## (10,12] (12,14] (14,16] (16,18] (18,20] (20,22] (22,24] (24,26] (26,28] (28,30] 
##       2       1       7       3       5       5       2       2       1       0 
## (30,32] (32,34] 
##       2       2

3.2 Bar Charts

n <- table(mtcars$gear)

barplot(n,xlab="Number of Gears")

3.3 Stem and Leaf Plots

We can add scale = 3 to make this line up properly

stem(mtcars$hp, scale = 3)
## 
##   The decimal point is 1 digit(s) to the right of the |
## 
##    5 | 2
##    6 | 2566
##    7 | 
##    8 | 
##    9 | 1357
##   10 | 59
##   11 | 0003
##   12 | 33
##   13 | 
##   14 | 
##   15 | 00
##   16 | 
##   17 | 555
##   18 | 000
##   19 | 
##   20 | 5
##   21 | 5
##   22 | 
##   23 | 0
##   24 | 55
##   25 | 
##   26 | 4
##   27 | 
##   28 | 
##   29 | 
##   30 | 
##   31 | 
##   32 | 
##   33 | 5

4 Fancier Output

Check out this fun stuff! Makes things look much cleaner.

4.1 Table Output

Categorical

hair <- table(starwars$hair_color)%>% 
  data.frame()

colnames(hair)[1] <- "Hair Color"

gt(hair)
Hair Color Freq
auburn 1
auburn, grey 1
auburn, white 1
black 13
blond 3
blonde 1
brown 18
brown, grey 1
grey 1
none 37
unknown 1
white 4

Or quantitative

bins <- seq(10,34,by = 2)

mpg <- cut(mtcars$mpg,bins)

table(mpg)%>%
  data.frame() %>% 
  gt()
mpg Freq
(10,12] 2
(12,14] 1
(14,16] 7
(16,18] 3
(18,20] 5
(20,22] 5
(22,24] 2
(24,26] 2
(26,28] 1
(28,30] 0
(30,32] 2
(32,34] 2

4.2 Summary Statistics

Using our classic mtcars dataset.

mtcars%>% select(mpg, cyl,hp) %>% 
  tbl_summary(statistic = list(all_continuous() ~ c("{mean} ({sd})",
                                                    "{median} ({p25}, {p75})",
                                                    "{min}, {max}"),
                              all_categorical() ~ "{n} / {N} ({p}%)"),
              type = all_continuous() ~ "continuous2"
  )
Characteristic N = 321
mpg
    Mean (SD) 20.1 (6.0)
    Median (IQR) 19.2 (15.4, 22.8)
    Range 10.4, 33.9
cyl
    4 11 / 32 (34%)
    6 7 / 32 (22%)
    8 14 / 32 (44%)
hp
    Mean (SD) 147 (69)
    Median (IQR) 123 (97, 180)
    Range 52, 335
1 n / N (%)

4.3 Histograms

4.3.1 ggplot

ggplot(mtcars, aes(mpg))+ 
  geom_histogram(binwidth = 2,col = 'black', fill = 'darkblue', alpha = 0.75)+
  labs(title = 'Distribution of Miles Per Gallon', caption = "1974 Motor Trend US Magazine")+
  theme_bw()

4.3.2 plot_ly

Since this is an interactive graph, it will not show up in a .pdf file, but it is great to look at in an .html document.

plot_ly(x = ~mtcars$mpg, type = "histogram", alpha = 0.6) %>% 
  layout(title = 'Distribution of Miles Per Gallon',
         xaxis = list(title = 'Miles Per Gallon'),
         yaxis = list(title = 'Count'))

4.4 Boxplots

I think the plotly version of a boxplot is superior since it is interactive.

plot_ly(y = starwars$height, type = 'box', name = 'Height [cm]',text = starwars$name) %>% 
  layout(title = 'Distribution of Star Wars Character Heights')

4.5 Correlation

reduced <- mtcars %>% 
  select(mpg, hp, wt,qsec,disp,drat)

corrplot(cor(reduced),
         type = "lower",
         order = "hclust", 
         tl.col = "black",
         tl.srt = 45,
         addCoef.col = "black",
         diag = FALSE)

4.6 Scatterplots

4.6.1 ggplot

ggplot(starwars,aes(height, mass))+
  geom_point(color = 'gray40')+
  theme_bw()+
  labs(title = "Relationship between Mass and Height of Star Wars Characters")

4.6.2 plotly

plot_ly(starwars, y = ~mass, x = ~height, type = 'scatter',text = ~name, mode = "markers")